Everyone remember weapon speed? Well we played for several years in a game where initiative was calculated by brief algebraic equation to generate a number between 1 and 10
[(10+ws)/2] - dex bonus, with multiple attack happening half way toward te end orf the round.
So my halflng rolls a 5 with his short sword and a dex bonus of 2... he goes on 2 (5+3)/2)-2, and again on 6 if he ha another attack, and again on 8 if he has a third.
Movement was done 12' per initiative number(2.5 squares on the battle map), and if your spellcaster declared multiple spellcasting he could roll a d4 + the casting time and just cast again then, or d6 + ct for a new spell.
Another quirky rule: if you rolled a '0', which was very possible, you could roll again, andother '0', and you could roll again wihtthe lowest possible outcome being a 1. At that point you had two fee attacks or maybe even movements on zero... except for missile fire, which could only get one.
I had a halfling with 19 dex for the entire game and he routinely got 4 or 5 attacks off in a round with daggers...
Also, we died. A lot.
The game was wonderful, but I prefer the old d20 + your modifier personally...